Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions-Reference-Cited by-同舟云学术

Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions

Published:2023-09-26 Issue:10 Volume:12 Page:915
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Almoneef Areej A.¹^ORCID,Abdel-Baky Rashad A.²

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

2. Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt

Abstract

This study utilizes the axodes invariants to derive novel hyperbolic proofs of the Euler–Savary and Disteli formulae. The inflection circle, which is widely recognized, is situated on the hyperbolic dual unit sphere, in accordance with the principles of the kinematic theory of spherical locomotions. Subsequently, a timelike line congruence is defined and its spatial equivalence is thoroughly studied. The formulated assertions degenerate into a quadratic form, which facilitates a comprehensive understanding of the geometric features of the inflection line congruence.

Funder

Princess Nourah bint Abdulrahman University Researchers Supporting Project

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/10/915/pdf

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